Hi OP, look at the course structure and see how science heavy it is. For example Oxford's course is very science based (bit obvious as it's called Experimental Psychology), Bristol is the same. I don't know of any unis that require you to have studied psychology before and many don't count it as a respected a level subject but do prefer you to have core sciences or maths. It's very competitive but just make sure you read around the subject and write an amazing personal statement, check what the unis you want to apply to are looking for in an applicant.
Feel free to message me if you have more specific questions/want more advice. I received all 5 offers this year from Oxford, UCL, Bath, Southampton and Cardiff.